Even as fixed income yields spike and concerns rise about an ongoing "taper tantrum" type of event, money continues to flow into bond funds.

A net of $5.3 billion in fresh cash has hit bond mutual and exchange-traded funds in June, even though collectively they are down close to 1 percent, according to a tally from market data firm TrimTabs.

"The lack of reaction to the backup in bond yields since mid-April is startling," David Santschi, TrimTabs CEO, said in a statement. "We would normally expect investors to be selling hard by now."

The 10-year U.S. Treasury note, considered a benchmark for the broader fixed income market, touched a 2.45 percent yield Tuesday morning, its highest since Oct. 3. The move has come amid concerns that the Federal Reserve is getting closer to liftoff—though some on Wall Street expect the move to be more like a "crawl"—of its own benchmark funds rate.

If the U.S. central bank does move in 2015, it will be the first time in nine years that the Fed has raised rates, as part of a zero interest rate policy in place since late 2008.

The biggest winner among bond ETFs has been the iShares Core U.S. Aggregate Bond fund, which has taken in about $403.9 million, the fifth most of all ETFs, so far in June, according to FactSet data compiled on ETF.com.

Not all bond ETFs have been winners, though. Investors are showing a conservative mindset, dumping junk and long-duration government bonds:

Bond ETF winners and losers

Fund

Ticker

Flows ($million +/-)

iShares Core U.S. Aggregate Bond

AGG

408.9

iShares Short Maturity Bond

NEAR

235.4

SPDR Barclays High Yield Bond

JNK

-475.8

iShares iBoxx $HY Corp Bond

HYG

-439.5

iShares 20+ Year Treasury Bond

TLT

-370.9

Source: FactSet/ETF.com

The overall penchant for bonds is worrying some strategists.

"Global growth, inflation and interest rates are rebounding, and we are only a few months away from likely Fed liftoff. As result corporate bond prices are declining at a pace eerily similar to what we saw during the Taper Tantrum in (October) 2013," Hans Mikkelsen, credit strategist at Bank of America Merrill Lynch, said in a note to clients that referenced a spike in yields after former Fed Chairman Ben Bernanke tipped his hand about the end of the quantitative easing program.

"We think that markets are too complacent about the risks associated with the move higher in rates," he added.

Interestingly, BofAML, in the big picture, has a fairly benign view of the bond picture.

While holding a slightly underweight position in fixed income, the firm is looking for bond yields to turn around in fairly dramatic fashion, with the 10-year dropping to around the 1.957 percent range.